diff --git a/src/packaging/specifiers.py b/src/packaging/specifiers.py
index 13bc9bda..05ea893a 100644
--- a/src/packaging/specifiers.py
+++ b/src/packaging/specifiers.py
@@ -588,9 +588,9 @@ def _compare_greater_than(self, prospective: Version, spec_str: str) -> bool:
 
         # Ensure that we do not allow a local version of the version mentioned
         # in the specifier, which is technically greater than, to match.
-        if prospective.local is not None and _base_version(
+        if prospective.local is not None and _public_version(
             prospective
-        ) == _base_version(spec):
+        ) == _public_version(spec):
             return False
 
         # If we've gotten to here, it means that prospective version is both
diff --git a/tests/test_specifiers.py b/tests/test_specifiers.py
index f5949424..2407824d 100644
--- a/tests/test_specifiers.py
+++ b/tests/test_specifiers.py
@@ -398,6 +398,17 @@ def test_comparison_non_specifier(self) -> None:
                 ("2!1.0", ">2.0"),
                 # Test some normalization rules
                 ("2.0.5", ">2.0dev"),
+                # Test local versions with pre/dev/post segments and >
+                # (verifies _public_version keeps pre/dev/post in the guard)
+                ("1.0+local", ">1.0.dev1"),
+                ("4.1.0a2.dev1235+local", ">4.1.0a2.dev1234"),
+                ("1.0a2+local", ">1.0a1"),
+                ("1.0b2+local", ">1.0b1"),
+                ("1.0rc2+local", ">1.0rc1"),
+                ("1.0.post2+local", ">1.0.post1"),
+                ("1.0.dev2+local", ">1.0.dev1"),
+                ("1.0a1.dev2+local", ">1.0a1.dev1"),
+                ("1.0.post1.dev2+local", ">1.0.post1.dev1"),
             ]
         ]
         + [
@@ -465,7 +476,16 @@ def test_comparison_non_specifier(self) -> None:
                 ("2.0.post1", ">2"),
                 ("2.0.post1.dev1", ">2"),
                 ("2.0+local.version", ">2"),
-                ("1.0+local", ">1.0.dev1"),
+                ("4.1.0a2.dev1234+local", ">4.1.0a2.dev1234"),
+                # Test local versions with pre/dev/post segments and >
+                # (local variant of the exact spec version must not match)
+                ("1.0a1+local", ">1.0a1"),
+                ("1.0b1+local", ">1.0b1"),
+                ("1.0rc1+local", ">1.0rc1"),
+                ("1.0.post1+local", ">1.0.post1"),
+                ("1.0.dev1+local", ">1.0.dev1"),
+                ("1.0a1.dev1+local", ">1.0a1.dev1"),
+                ("1.0.post1.dev1+local", ">1.0.post1.dev1"),
                 # Test the less than operation
                 ("2.0.dev1", "<2"),
                 ("2.0a1", "<2"),